What is the recommended approach for fitting a CFA model that contains multiple groups, each group pointing to a different set of indicators?

Specifically, I have 6 latent variables that map to a set of approximately 20 indicators. However, there are three subgroups within the dataset that contain differing sets of indicators, i.e., one group may be missing a subset of indicators (MNAR), while another group may be missing another, etc. There are three such clearly defined subgroupings.

Is the only solution to fit separate CFA models for each of these three patterns?